2000/05/31 by A. A'Campo-Neuen, J. Hausen, S. Schroeer
Mathematics · #math.AG #msc:14M25 #msc:14C20 #msc:14L30 #msc:14L32
published as Math. Nachr. 246-247, 5-19 (2002) · minor changes, to appear in Math. Nachr., 13 pages, 2 figures
arxiv created 2001/08/06 · arxiv updated 2009/11/30
Generalizing cones over projective toric varieties, we present arbitrary toric varieties as quotients of quasiaffine toric varieties. Such quotient presentations correspond to groups of Weil divisors generating the topology. Groups comprising Cartier divisors define free quotients, whereas \QQ-Cartier divisors define geometric quotients. Each quotient presentation yields homogeneous coordinates. Using homogeneous coordinates, we express quasicoherent sheaves in terms of multigraded modules and describe the set of morphisms into a toric variety.